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A110914
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"Self convolution mod 3" of central Delannoy numbers (see comment).
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0
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1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4, 0, 2, 0, 4, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4, 0, 8, 0, 16, 0, 8, 0, 4, 0, 8, 0, 4, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n)=sum(k=0,n,{b(k)*b(n-k)} mod 3) where b(k)=sum(k=0,n,binomial(n,k)*binomial(n+k,k)) are the central Delannoy numbers. The formula is obtained using techniques described in the Deutsch-Sagan paper.
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LINKS
| E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215.
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FORMULA
| a(2n-1)=0 and a(2n)=2^t_1(n) where t_1(n) denotes the number of 1's in the ternary representation of n (A062756). Recurrence : a(3n)=a(n), a(3n+1)=a(n-1), a(3n+2)=2*a(n)
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PROG
| (PARI) b(n)=sum(k=0, n, binomial(n, k)*binomial(n+k, k)); a(n)=sum(k=0, n, (b(k)*b(n-k))%3)
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CROSSREFS
| Cf. A062756.
Sequence in context: A158945 A156667 A178090 * A193527 A127505 A194923
Adjacent sequences: A110911 A110912 A110913 * A110915 A110916 A110917
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 04 2005
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